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Register a new userSecular dynamics of binaries in stellar clusters I: general formulation and dependence on cluster potential
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Chris Hamilton DAMTP
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Orbital evolution of binary systems in dense stellar clusters is important in a variety of contexts: origin of blue stragglers, progenitors of compact object mergers, millisecond pulsars, and so on. Here we consider the general problem of secular evolution of the orbital elements of a binary system driven by the smooth tidal field of an axisymmetric stellar cluster (globular, nuclear, etc.) in which the binary orbits. We derive a secular Hamiltonian (averaged over both the inner Keplerian orbit of the binary and its outer orbit within the cluster) valid to quadrupole order for an arbitrary cluster potential and explore its characteristics. This doubly-averaged tidal Hamiltonian depends on just two parameters, which fully absorb the information about the background cluster potential and the binarys orbit within it: a dimensional parameter $A$ setting the secular timescale, and a dimensionless parameter $Gamma$ which determines the phase portrait of the binarys inner orbital evolution. We examine the dependence of $A$ and $Gamma$ on cluster potential (both spherical and axisymmetric) and on the binary orbit within the cluster. Our theory reproduces known secular results - such as Lidov-Kozai evolution and the effect of the Galactic tide on Oort Cloud comets - in appropriate limits, but is more general. It provides a universal framework for understanding dynamical evolution of various types of binaries driven by the smooth tidal field of any axisymmetric potential. In a companion paper (Hamilton & Rafikov 2019b) we provide a detailed exploration of the resulting orbital dynamics.
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Secular evolution of binaries driven by an external (tidal) potential is a classic astrophysical problem. Tidal perturbations can arise due to an external point mass, as in the Lidov-Kozai (LK) theory of hierarchical triples, or due to an extended stellar system (e.g. galaxy or globular cluster) in which the binary resides. For many applications, general-relativistic (GR) apsidal precession is important, and has been accounted for in some LK calculations. Here we generalise and extend these studies by exploring in detail the effect of GR precession on (quadrupole-level) tidal evolution of binaries orbiting in arbitrary axisymmetric potentials (which includes LK theory as a special case). We study the (doubly-averaged) orbital dynamics for arbitrary strengths of GR and binary initial conditions and uncover entirely new phase space morphologies with important implications for the binary orbital evolution. We also explore how GR precession affects secular evolution of binary orbital elements when the binary reaches high eccentricity ($eto 1$) and delineate several different dynamical regimes. Our results are applicable to a variety of astrophysical systems. In particular, they can be used to understand the high-eccentricity behaviour of (cluster) tide-driven compact object mergers -- i.e. LIGO/Virgo gravitational wave sources -- for which GR effects are crucial.
Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system driven by the global tidal field of an axisymmetric stellar cluster in which the binary orbits. In a companion paper (Hamilton & Rafikov 2019a) we developed a general Hamiltonian framework describing such systems. The effective (doubly-averaged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter $Gamma$. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as $Gamma$ is varied. We find that for $Gamma > 1/5$ the phase-space structure and the evolution of binary orbital element are qualitatively similar to the Lidov-Kozai problem. However, this is only one of four possible regimes, because the dynamics are qualitatively changed by bifurcations at $Gamma = 1/5,0,-1/5$. We show how the dynamics are altered in each regime and calculate characteristics such as secular evolution timescale, maximum possible eccentricity, etc. We verify the predictions of our doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular timescale should exceed the period of the binary around the cluster by $gtrsim 10-10^2$ (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harboured by stellar clusters.
The angular momentum evolution of stars close to massive black holes (MBHs) is driven by secular torques. In contrast to two-body relaxation, where interactions between stars are incoherent, the resulting resonant relaxation (RR) process is characterized by coherence times of hundreds of orbital periods. In this paper, we show that all the statistical properties of RR can be reproduced in an autoregressive moving average (ARMA) model. We use the ARMA model, calibrated with extensive N-body simulations, to analyze the long-term evolution of stellar systems around MBHs with Monte Carlo simulations. We show that for a single-mass system in steady-state, a depression is carved out near an MBH as a result of tidal disruptions. Using Galactic center parameters, the extent of the depression is about 0.1 pc, of similar order to but less than the size of the observed hole in the distribution of bright late-type stars. We also find that the velocity vectors of stars around an MBH are locally not isotropic. In a second application, we evolve the highly eccentric orbits that result from the tidal disruption of binary stars, which are considered to be plausible precursors of the S-stars in the Galactic center. We find that RR predicts more highly eccentric (e > 0.9) S-star orbits than have been observed to date.
We derive the kinetic equation that describes the secular evolution of a large set of particles orbiting a dominant massive object, such as stars bound to a supermassive black hole or a proto-planetary debris disc encircling a star. Because the particles move in a quasi-Keplerian potential, their orbits can be approximated by ellipses whose orientations remain fixed over many dynamical times. The kinetic equation is obtained by simply averaging the BBGKY equations over the fast angle that describes motion along these ellipses. This so-called Balescu-Lenard equation describes self-consistently the long-term evolution of the distribution of quasi-Keplerian orbits around the central object: it models the diffusion and drift of their actions, induced through their mutual resonant interaction. Hence, it is the master equation that describes the secular effects of resonant relaxation. We show how it captures the phenonema of mass segregation and of the relativistic Schwarzschild barrier recently discovered in $N$-body simulations.
Radiative feedback is an important consequence of cluster formation in Giant Molecular Clouds (GMCs) in which newly formed clusters heat and ionize their surrounding gas. The process of cluster formation, and the role of radiative feedback, has not been fully explored in different GMC environments. We present a suite of simulations which explore how the initial gravitational boundedness, and radiative feedback, affect cluster formation. We model the early evolution ($<$ 5 Myr) of turbulent, 10$^6$ M$_{odot}$ clouds with virial parameters ranging from 0.5 to 5. To model cluster formation, we use cluster sink particles, coupled to a raytracing scheme, and a custom subgrid model which populates a cluster via sampling an IMF with an efficiency of 20% per freefall time. We find that radiative feedback only decreases the cluster particle formation efficiency by a few percent. The initial virial parameter plays a much stronger role in limiting cluster formation, with a spread of cluster formation efficiencies of 37% to 71% for the most unbound to the most bound model. The total number of clusters increases while the maximum mass cluster decreases with an increasing initial virial parameter, resulting in steeper mass distributions. The star formation rates in our cluster particles are initially consistent with observations but rise to higher values at late times. This suggests that radiative feedback alone is not responsible for dispersing a GMC over the first 5 Myr of cluster formation.
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